// Calculation Program for calculating shape of a flower with the use of a Cardioid (1), July 15, 2012

// file name: flower_g.c

#include< stdio.h>
#include< math.h>

void main(void)
{
	double a,pi;// "a" is the constant of original Cardioid and pi=3.1415...
	double t,dt;// the phase angle and its increment of the Cardioid before the conversion respectively
	double r,z;// the moving radius and the phase angle of the Cardioid after some conversion respectively
	double f;// the phase angle of the Cardioid after the final conversion into a horned one (using as a petal of a flower)
	int n;// a desired numbers of petals of a flower
	double alpha;// the angle for the horned Cardioid (used as that alpha=2*pi/n (using as "alpha=pi/n" in this C program)
	double tmin,tmax;// the minimum and maximum values of the phase angle "t" respectively
	int i,imax,j;
	double x,y;// the orthogonal coordinates of a petal before contraction or expansion
	float b;// the ratio of contraction or expansion of a petal in the length direction
	float c;// the radius of a center circle
	double beta;// angular range to be occupied by a petal around the center circle
	double dbeta;// increment of "beta"
	double k;// magnification factor of the criterion angle "alpha=2*pi/n" where 0 < k
	double l;// magnification factor of the angular range "beta" where 0 < l 
	double rr;// the moving radius of a petal after contraction or expansion
	double ff;// the phase angle of a petal after contraction or expansion
	double p;// phase angle of center circle
	double dp;// increment of "p"
	int nz;// division numbers of both phases "z" and "beta"
	int m;// count numbers of the increment of "beta"
	double xx[30001],yy[30001];// Take care of the upper limit of storage memory capacitance.

	FILE *fp;

// setting of the constants
	pi=3.14159265;
	a=1.;

// setting of the other parameters
	printf("Input the numbers of petals. \n n=? ");
	scanf("%d",&n);
	printf("n=%d\n",n);
	printf("\n");

	alpha=2*pi/n;// the angle for the horned Cardioid as a petal
	beta=alpha;// fundamentally criteria value of "beta" is supposed to be equal to "alpha".

	k=1.5;// k=1 magnification factor of the criterion angle 'alpha=2*pi/n' where 0 < k
	l=0;// l=0 magnification factor of the criterion angular range "beta" where 0 < l

	alpha=k*alpha;// the magnificated angle of the botom of the petal
	beta=l*beta;// the magnificated angular range to be occupied by a petal around the center circle

	printf("Input the ratio of contraction or expansion of a petal in the length direction. \n b= ? ");
	scanf("%f",&b);
	printf("b=%f\n",b);
	printf("\n");

	printf("Input the radius of the center circle. \n c= ? ");
	scanf("%f",&c);
	printf("c=%f\n",c);
	printf("\n");

	tmin=-pi/2;
	tmax=3*pi/2;

	nz=200;

	dt=(tmax-tmin)/nz;// // plotting interval of "t"
	dbeta=beta/nz;// increment of "beta"

	dp=2*pi/n/20;// increment of "p"

// execution of calculation
	i=0;

	for(j=1;j<=n;j++) // sweep of n numbers of petals
	{
		m=0;

		for(t=tmin;t<=tmax+dt;t=t+dt) // sweep of phase angle "t" of the each petal
		{
			i++;
			m++;

			if(t>(3*pi/2-dt) && t<(3*pi/2+dt))
			{
				r=0.;
				z=-pi/2;
			}
			else
			{
				if(t>(-pi/2-dt) && t<(-pi/2+dt))
				{
					r=0.;
					z=pi/2;
				}
				else
				{
					r=a*sqrt((5-3*sin(t))*(1+sin(t)));
					z=asin(a*(1-sin(t))*cos(t)/r);
				}
			}
			
			f=-alpha*z/pi+pi/2;

			x=r*cos(f);
			y=b*r*sin(f);

			rr=sqrt(x*x+y*y);

			if(fpi||ff<0)
					{
						ff=atan(b*tan(f));
					}
*/
				}
			}

			ff=ff+2*pi*(j-1)/n;

			xx[i]=r*cos(ff)+c*cos(2*pi*(j-1)/n+pi/2-beta/2+m*dbeta);
			yy[i]=r*sin(ff)+c*sin(2*pi*(j-1)/n+pi/2-beta/2+m*dbeta);

			printf("i=%d,x=%f,y=%f\n",i,xx[i],yy[i]);
		}

		if(l<=1) // Simply for drawing an additional circle of underlying petal.
		{
			for(p=2*pi*(j-1)/n+pi/2+beta/2;p<2*pi*j/n+pi/2-beta/2+dp;p=p+dp)
			{
				i++;

				xx[i]=c*cos(p);
				yy[i]=c*sin(p);

				printf("i=%d,x=%f,y=%f\n",i,xx[i],yy[i]);
			}
		}
		else
		{
			for(p=2*pi*(j-1)/n+pi/2+beta/2;p>2*pi*j/n+pi/2-beta/2-dp;p=p-dp)
			{
				i++;

				xx[i]=c*cos(p);
				yy[i]=c*sin(p);

				printf("i=%d,x=%f,y=%f\n",i,xx[i],yy[i]);
			}
		}
	}

	imax=i;

// writing the calculated coordinates data of the curve into a textfile named "flower_g.txt"
	fp=fopen("flower_g.txt","w");
	if(fp==NULL)
		{
		printf("FILE OPEN ERROR\n");
		}
	else
		{
		for(i=1;i<=imax;i++)
			{
			fprintf(fp,"%f,%f\n",xx[i],yy[i]);
			}
		fflush(fp);
		fclose(fp);
		}
	printf("end\n");
}// the end of the program

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